What's more, positive tweets about vaccines sometimes had the opposite effect — a high number of pro-vaccine posts seemed to encourage people to tweet negatively about vaccines, said study researcher Marcel Salathé, an assistant professor of biology at Penn State University.

"In other words, pro-vaccine messages seemed to backfire when enough of them were received," Salathé said.

The reason for this phenomenon is not clear. But it's possible that “many people had latent negative opinions about the vaccine, and when they were intensely exposed to enough positive messages, they felt the need to express their negative sentiment," Salathé said.

Future studies may reveal what it is about negative tweets that makes them contagious. The results of those studies could help public health officials “send positive messages in a way that would be more likely to have the intended effect," Salathé said.